Nonlinear, Adiabatic Process, And The Nonlocality Of Quantum Theory Research

In this dissertation we studied several basic theoretical problems in the field of quantum mechanics. This includes nonlinearity of Kerr medium, time-dependent adiabatic process and quantum nonlocality. The main context includes:At first, based on the nonlinear map defined, we present a new calculation approach in which the nonlinear transformation operator including N² in the exponent can be transformed identically into a linear transformation operator under the normal ordered form including N in the exponent, we can calculate the time-evolution case with continuously varied imaginary parameter t in the exponent which enables an analytical calculation of the dynamical evolution of arbitrary initial states in a simple way, and we also derive the quantum partition function of Kerr medium where the parameter t in the exponent is imaginary.Secondly, according to the definition of adiabatic orbit, adiabatic evolution orbit and expanding with adiabatic invariant basis, we propose a general quantum adiabatic theory. The probabilities keeping in the adiabatic orbit is obtained in the first-order and second-order, respectively. We also give concise and convenient adiabatic conditions and calculate some examples with this adiabatic conditions. Meanwhile, we point out that the geometric potential in the new adiabatic conditions are of abundant physical and geometric meanings.At last, we propose a Bell-CHSH inequality of continuous variables based on parity-coherent states of light field. The Bell operator based on parity-coherent states acts on entangled coherent and the violation value of this inequality will reach its upper limit 2 2^1/2. The required parity-coherent states are experimentally realizable. Meanwhile, when we find the optimal Bell operator of entangle coherent state, the violation will reach a constant 2 2^1/2 when the mean number of photons is large.